Pauli's exclusion principle:

No 2 electrons in an atom can have identical quantum numbers. This is an example of a general principle which applies not only just to electrons but also to other particles of half-integer spin. It does not apply to the particles of integer spin. The Pauli Exclusion Principle is part of 1 of our most basic observations of nature: particles of half-integer spin should have antisymmetric wave functions, and particles of integer spin should have symmetric wave functions. Pauli's Principle is based on the fact that any 2 given electrons are indistinguishable from one another and therefore changing the designations between 2 or more electrons in different quantum states should have no observable effect. In addition, in describing the wave function of an atom -- which is the product of the wave functions of individual electrons.

Quantum Physics mandates that the wave function itself (of the atom or electron) is also not observable.The Pauli Exclusion Principle helps explain a wide range of physical phenomena. One particularly significant consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the range of chemical elements and their chemical combinations. An electrically neutral atom contains bound electrons which are equal in number to the protons in the nucleus. As electrons are fermions, the Pauli exclusion principle forbids them from occupying the same quantum state, so electrons have to pile on top of each other within an atom.

 The Pauli Exclusion Principle then specifies the wave functions of protons, electrons, and other so-called spin-1/2 particles to be anti-symmetric. Thus when 2 electron designations are switched in the same atom or molecule, the total wave function of the atom or molecule changes sign. Further, when 2 atoms come within close proximity to one another, the concept of each being in a separate state loses its meaning. Thus 2 atoms with closed shells find they cannot form a chemical bond as the electrons in 1 atom find no available quantum states in the other in which to occupy.